Equations of Higher Degree

Quadratic equation of Class 11

Equations of Higher Degree

An equation of degree n can be represented

as F(x) = a0xn + a1xn-1 + a2xn-2 + . . . + an = 0

with a0, a1, a2 . . . an ∈ C and a0 ≠ 0.

Then F(x) can be expressed as F(x) = a0 (x-α1) (x-α2) . . . (x-αn) implying that it will have exactly n roots (No more, no less)

Also the roots are connected by the relations α1 + α2 + … + αn =

Σ α1α2 = Equations of Higher Degree Σ α1α2α3 = -etc.

For example if α, β, γ are the roots of a cubic equation ax3 + bx2 + cx + d = 0

Then α + β + γ = Equations of Higher Degree, αβ + βγ + γα = and αβγ = -.

This situation prevails in equations of any finite degree.

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